The two principal uses of nuclear magnetic resonance (NMR) in medicine, namely magnetic resonance imaging (MRI) and in vivo NMR spectroscopy are making great strides, and MRI in particular has become an accepted and valued method of diagnostic radiology. The long term objective of this research is to enable state-of-the-art medical NMR systems to be installed in all major hospitals and their use brought to a wider range of patient care, indeed to all who need it. However the siting of whole-body NMR systems in hospitals presents substantial problems partly on account of the magnetic interference of the environment, and partly on account of the stray magnetic field generated by the magnet systems. There is often no alternative to placing the magnet system in a congested hospital environment and in these cases a solution is provided by surrounding the magnet with a magnetic shield. A few whole-body magnets have been shielded in an essentially empirical manner using shields of enormously different size and cost, but no scientific analysis has been made to discover the optimum screening system, or to calculate the detailed effects of the screen on the crucial uniformity of field in the magnet bore or on the stray field around the system. The specific objective of this proposed research is to analyze scientifically and systematically a range of shields of various shapes, size and constitution to discover the optimum system. Specific questions to be answered will be (a) What is the best geometrical configuration of the shield? (b) Should it be fitted closely over the magnet or remote from it? (c) What dimensional and magnetic tolerances will be consistent with the required field uniformity? (d) What are the best materials for the shield? (e) What forces does the screen impose on the magnet windings? Consideration will be given to effects on field gradient switching and to the use of active screens. The initial approach will be theoretical, and when the answers become more clear, will be followed by experimental verification.